Thanks Kashish - I can't see any details re: my query here though?
Can you please try these steps:
1. From the Server Menu -> Sign In option -> Sign out (not from the workbook's bottom sign-out)
2. From the Server Menu -> Sign In -> type the website as: https://public.tableau.com/
If it does not ask for your credentials, which happens mostly when sign-out and sign-in immediately back, then make sure you sign-out again as in step 1.
(This is the most important step which I noticed during my ordeal for around 3 hours)
3. Provide your credentials again to sign-in
4. Now Save the workbook either using Server -> Tableau Public -> Save to or Save As option.
I tested these steps for the first time publish as well as after publishing -> making changes.
thanks for you help! Unfortunately this did not work. I think it might be a local problem - I have edited above.